Lúcia is using energy at a rate of $420$ kilocalories $(\text{kcal})$ per hour $(\text{h})$ ice skating. At what rate is Lúcia using energy in calories per minute $\left(\dfrac{\text{cal}}{\text{min}}\right)$ ?
Answer: We will convert $420\,\dfrac{\text{kcal}}{\text{h}}$ to a rate in $\dfrac{\text{cal}}{\text{min}}$ using the following conversion rates: There are $60\text{ min}$ per $1\text{ h}$. There are $1000\text{ cal}$ per $1\text{ kcal}$. $\begin{aligned} &\phantom{=} \dfrac{420 \text{ kcal}}{1\text{ h}} \cdot\dfrac{1\text{ h}}{60\text{ min}}\cdot\dfrac{1000\text{ cal}}{1\text{ kcal}} \\\\ &=\dfrac{420\cdot 1 \cdot 1000 \cdot \cancel{\text{kcal}}\cdot\cancel{\text{h}} \cdot \text{cal}}{1\cdot 60 \cdot 1\cdot\cancel{\text{h}}\cdot \text{min} \cdot \cancel{\text{kcal}} } \\\\ &=\dfrac{420{,}000}{60}\,\dfrac{\text{cal}}{\text{min}} \\\\ &=7000\,\dfrac{\text{cal}}{\text{min}} \end{aligned}$ In conclusion, Lúcia is using energy in $\dfrac{\text{cal}}{\text{min}}$ at a rate of: $7000\,\dfrac{\text{cal}}{\text{min}}$